This course covers the basic algebra and technological tools used in the social, physical and life sciences to analyze quantitative information. The emphasis is on real world, open-ended problems that involve reading, writing, calculating, synthesizing, and clearly reporting results. Topics include descriptive statistics, linear, and exponential models. Technology used in the course includes computers (spreadsheets, internet) and graphing calculators.

This course teaches the algebraic and conceptual skills students need to master before they are ready for MATH 134 or MATH 135. The major part of the course then involves the application of linear, quadratic, and exponential models to problems in management and economics.

Math Placement Test or MATH 115 with a grade of B or better in the previous semester.

Students intending to take Calculus I and II (MATH 140 and 141) should take MATH 130 instead of MATH 129. Students may take MATH 130 after MATH 129, but only with the explicit permission of the department, and then only for two credits.

Math Placement Test or MATH 115 with a grade of B or better in the previous semester.

No student receives graduation credits for MATH 130 if it is taken after successful completion of any higher math course. Students who have successfully completed MATH 130 may not subsequently take MATH 129 for credit. Students may take MATH 130 after MATH 129 only with explicit permission of the department, and then only for two credits.

A one-semester course in calculus, with particular emphasis on applications to economics and management. Topics covered include limits, continuity, derivatives, and integrals.

Math Placement Test or successful completion of MATH 129 or MATH 130.

Students may not receive graduation credit for both MATH 134 and MATH 135. Students may take MATH 140 after MATH 134, but only with the explicit permission of the department and then only for two credits.

Calculus developed intuitively and applied to problems in biology, economics, psychology, and geometry. A course for non-physical science and non-mathematics majors. Suitable for some pre-medical programs.

Math Placement Test or MATH 130.

No student receives graduation credit for MATH 135 if it is taken after successful completion of MATH 134 or 140 or a higher Math course. Students may take MATH 140 after 135 only with explicit permission of the Department, and then only for two credits.

This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and uses it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions.

Math Placement Test or completion of MATH 130 within the past semester with a grade of B or higher.

A student who has received credit for either MATH 134 or MATH 135 may not take MATH 140 for credit without the explicit permission of the department and then only for two credits.

The course is the first in the sequence of calculus courses for science and math majors. The topics covered in this course parallel the topics covered in the other Math 140 sections; however, the applications presented in this course have origins in biological systems. The course begins with the basic concepts of functions, discrete time models and limits in the context of population models. Further topics covered include: derivatives along with their applications to biological modeling and definite and indefinite integrals with applications to geometric and biological problems.

Math Placement Test or a grade of B or better in MATH 130 in the previous semester.

Students who complete this course will be eligible for MATH 141, or MATH 146, as well as MATH 303.

The course is the second in the sequence of calculus courses for life science and environmental science majors. The topics covered in this course do not parallel the topics covered in the Math 141: Calculus II sections; however, the material covered in this course introduces the student to mathematical fields that are commonly applied in the study of life and environmental sciences. Applications presented in this course have origins in biological and environmental systems. The course begins with a brief review of integration techniques learned in Calculus I, and continues with a thorough analysis of integration. Computational methods, differential equations, linear algebra and multivariable calculus are introduced so that the student may examine dynamical systems that are central to understanding the behavior of many physical models.

MATH 140 or MATH 145.

This course does not fulfill the Calculus II (Math 141) requirement and does not serve as a prerequisite for Multivariable Calculus (Math 240). This course satisfies the following GenEd requirements: Quantitative Reasoning, Distribution II: MT.

Because MATH 240 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. No student receives graduation credit for MATH 240 if it is taken after successful completion of MATH 242. Students may take MATH 242 after MATH 240 only with the explicit permission of the Department and then only for one credit.

Because MATH 242 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. No student receives graduation credit for MATH 240 if it is taken after successful completion of MATH 242. Students may take MATH 242 after MATH 240 only with the explicit permission of the Department and then only for one credit.

This course is an introduction to discrete structures in mathematics. Topics include, but are not limited to: basic combinatorial structures and analysis; elementary number theory; sequences and operations with sequences; graphs and trees; equivalence and partial orders.

A comprehensive study of the nature of ordinary differential equations. The course includes qualitative analysis of properties of solutions, as well as standard methods for finding explicit solutions to important classes of differential equations. It presents many applications, particularly for linear equations.

The purpose of this course is to develop a basic skillset in using computer software to approach, analyze, and report on mathematical problems. Students will learn to work collaboratively to investigate both basic problems and advanced mathematical topics via simulation and numerical exploration, and they will prepare professional level reports which compile and communicate their results. The topics and their applications will be illustrated using computer algebra software (e.g. Sage), a modern programming language (e.g. Python), and document creation software (e.g. LaTeX).

Mathematical models of population growth and other biological processes and nth order linear difference equations will be used to model propagation of annual plants; growth of segmental organisms; red blood cell production; and population growth and destiny dependence in single-species populations. Continuous models will be constructed from among several possibilities, including the logistic equation, simple exponential growth, the Chemostat, Michaelis-Menten kinetics, drug delivery, glucose-insulin kinematics, Gompertz growth in tumors, and the Fitzhugh-Magumo model for neural impulses. Appropriate software will be used throughout the course.

The course is designed to aid students in making the transition from calculus, differential equations and linear algebra to the more advanced and more abstract mathematics courses, such as abstract algebra and real analysis. The course will cover mathematical logic, mathematical proofs, mathematical induction, set theory, relations, functions, cardinality and applications of proofs in the study of such areas as number theory, calculus and group theory, as time permits.

This course presents the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal. Topics also include basic ideas and techniques of statistical analysis.

This is a statistics course for students with a firm mastery of calculus, emphasizing the mathematical and conceptual bases of statistics, with a view to understanding the proper application of standard methods. The course includes thorough treatments of the Central Limit Theorem, the theory of estimation, hypothesis testing, and regression.

Applied Partial Differential Equations is an introduction to the basic properties of partial differential equations and to some of the techniques that have been developed to analyze the solutions to these equations. The equations that describe the dynamics of waves, diffusion, flow and vibrations will be the main focus of this course. Initial value and boundary value problems of first and second-order equations will be considered. A geometric and analytic analysis of the solutions to these equations will be explored. Specific topics covered include classification of partial differential equations, well posed problems, the maximum principles for the diffusion equation and Laplace's equation, Dirichlet, Neumann and Robin boundary conditions, the method of characteristic coordinates, and separation of variables. The theory of Fourier Series will be introduced to the student and used to approximate solutions to inhomogeneous boundary value problems using the expansion method. Additional topics specific to the instructor's preference may be included in the course if time permits.

Differential geometry of curves and surfaces in Euclidean spaces, as an introduction to the geometry of Riemannian manifolds. The course presents intrinsic and extrinsic properties, both from a local and global point of view. Topics include; plane and space curves, surfaces, metrics on surfaces, Gaussian curvature, surfaces of constant curvature, shape operator, mean curvature and minimal surfaces, vector fields on surfaces.

Review of set theory and introduction to mathematical proof. Introduction to concepts and techniques of group theory, including but not limited to: symmetric groups, axiomatic definitions of groups, important classes of groups, subgroups, group homomorphisms, coset theory, normal subgroups, quotient groups, direct products, Sylow theorems. Possible applications include number theory, geometry, physics and combinatorics.

This course traces the development of mathematics from ancient times up to and including 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problem solving.

Fundamental concepts of evolutionary game theory and their application in biology. Topics include: the strategy and payoff matrix, the game tree, strategic and extensive form games, symmetric games, Nash equilibria. Evolutionary game theory concepts are discussed for two-strategy games (Prisoner's Dilemma, Hawk-Dove) and three-strategy games (Rock-Scissors-Paper). Biological examples are studied, such as blood sharing in vampire bats, competition in bacteria, or the evolution of altruistic punishment.

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

MATH 280 or permission of instructor.

Although this course is repeatable up to six credits, Mathematics majors (who are required to take a certain number of mathematics courses at the 300-level or higher) may count this course at most once toward their upper-level elective requirement.

This course is an introduction to combinatorics: a branch of mathematics that studies the existence, enumeration, analysis, and optimization of discrete structures that satisfy certain properties. Topics include counting distributions and colorings, sieve methods (such as inclusion-exclusion, for example), generating functions, partially ordered sets, and Ramsey theory. Additional topics may be included, such as permutation spaces, matching theory, and elementary graph theory.

This course is a continuation of linear algebra, towards topics relevant to applications as well as theoretical concepts. Topics to be discussed are algebraic systems, the singular value decomposition (SVD) of a matrix and some of its modern applications. We will discuss Principal component analysis (PCA) and its applications to data analysis. We will study linear transformations and change of basis. We will discuss complex vector spaces and Jordan canonical form of Matrices. We will discuss non-negative matrices and Perron-Frobenius Theory. We will explain multiple matrix factorisations, such as LU, QR, NMF. Finally we will discuss other applications such as the Fast Discrete Fourier Transform. For each of these topics we will discuss numerical computer algorithms and their implementations. In particular we will discuss in detail eigenvalue estimation, including iterative and direct methods, such as Hausholder methods, tri-diagonalzation, power methods, and power method with shifts. We will explain concepts of numerical analysis that are important to consider when we talk about the implementation of algorithms, such as stability and convergence. We will discuss iterative methods as well as direct ones, their advantages and disadvantages. The methods are their applications will be illustrated using a common programming language such as python and/or R.

This course is an introduction to the abstract theory of continuity and convergence, otherwise known as general (or point-set) topology. Topics include metric spaces and topological spaces, continuity, subspaces, product and quotient spaces, sequences, nets and filters, separation and countability, compactness, connectedness, and the fundamental group.

This is an introductory course on probability models with a strong emphasis on stochastic processes. The aim is to enable students to approach real-world phenomena probabilistically and build effective models. The course emphasizes models and their applications over the rigorous theoretical framework behind them, yet critical theory that is important for understanding the material is also covered. Topics include: discrete Markov chains, continuous-time Markov chains, Poisson processes, renewal theory, Brownian motion and martingales. Optional topics: queuing theory, reliability theory, and random sampling techniques. Applications to biology, physics, computer science, economics, and engineering will be presented.

This course will provide an introduction to methods in statistical learning that are commonly used to extract important patterns and information from data. Topics include, linear methods for regression and classification, regularization, kernel smoothing methods, statistical model assessment and selection, and support vector machines. Unsupervised learning techniques such as principal component analysis and generalized principal component analysis will also be discussed. The topics and their applications will be illustrated using the statistical programing language R.

A rigorous treatment of the calculus of functions of one real variable. Emphasis is on proofs. Includes discussion of topology of real line, limits, continuity, differentiation, integration and series.

This course is an introduction to the framework for modern advanced analysis. Topics include differentiable maps between Euclidean spaces, Implicit and Inverse Function Theorems, manifolds, differential forms, differentiation and integration on manifolds.

Work done by a student or group of students under faculty supervision on material not currently offered in a regularly scheduled course. Students wishing to undertake such work must first find a faculty member willing to supervise it; the work to be completed must be approved by the department chair.

An advanced course offering intensive study of selected topics in mathematics. A course offered as MATH 480 is an advanced undergraduate mathematics course being given for the first time and covering topics not available in current courses. Such a course is offered either to fulfill a one-time need or to try out material with the intention of developing a new course. Course content varies each semester and will be announced prior to registration.

An opportunity for qualified, advanced students to work on a specialized research project under the guidance of a faculty advisor.

Permission of Instructor.

Although this course is repeatable up to six credits, Mathematics majors (who are required to take a certain number of mathematics courses at the 300-level or higher) may count this course at most once toward their upper-level elective requirement.